Method of automatically tracking and photographing celestial objects and photographic apparatus employing this method

ABSTRACT

A celestial object is automatically tracked and photographed. Azimuth information of the celestial object is obtained relative to a photographic apparatus. First-tracking drive control data for performing a first-tracking photographing operation is calculated based on the azimuth information. The photographing operation is performed during a predetermined exposure time based on the first-tracking drive control data. After the photographing operation finishes, a first image taken in the photographing operation is obtained upon lapse of a predetermined time, and a second image corresponding to an ending of images taken by the photographing operation is obtained. An amount of deviation between a celestial object image in the first image and a corresponding celestial object image in the second image is calculated. A judgement is made as to whether a second-tracking photographing operation is to be performed based on a comparison between the deviation amount and a predetermined threshold.

CROSS-REFERENCE RELATED APPLICATIONS

The present application is a continuation of pending U.S. applicationSer. No. 13/117,517 filed May 27, 2011, the disclosure of which isincorporated by reference herein in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of automatically tracking andphotographing celestial objects which enables the capture of afreeze-frame picture of a celestial object(s) in long exposureastrophotography, and further relates to a photographic apparatusemploying this method.

2. Description of the Related Art

If long exposure astrophotography is carried out with a fixed camera(photographic apparatus), added light of stars during a long exposureform straight or curved light trails in the captured image, sincecelestial objects move relative to the camera due to the earth'srotation (diurnal motion). To carry out a long exposure in order tophotograph a celestial object so that the celestial object appears to bestill (stationary) relative to a photosensitive film or an image sensor(image pickup device), an equatorial equipped with an auto trackingsystem is generally used.

In recent years, a method of obtaining a still image of celestialobjects such as planets and stars in long exposure astrophotography hasbeen proposed in which a celestial object(s) is photographed a pluralityof times with a fixed digital camera without using an equatorial, andthereafter, the images thus obtained at the plurality of times are addedwhile correcting the positions of the celestial object(s) using data onthe obtained images (see Japanese Unexamined Patent Publications Nos.2006-279135 and 2003-259184).

However, an equatorial equipped with an auto tracking system isgenerally expensive, heavy and difficult to handle. The type of digitalcamera (disclosed in Japanese Unexamined Patent Publications Nos.2006-279135 and 2003-259184) which synthesizes a plurality of images hasinferior image registration accuracy and is slow in image processingspeed, and therefore, it is practically impossible to synthesize aplurality of astronomical images using only such a type of digitalcamera while performing tracking astrophotography.

SUMMARY OF THE INVENTION

The present invention provides a method of automatically tracking andphotographing celestial objects which enables the capture of a stillimage of a celestial object(s) such as a star or a planet in a statewhere each celestial object appears stationary with respect to a fixedpoint on the rotating Earth in long exposure astrophotography withoutusing an equatorial with a camera (photographic apparatus) directedtoward an arbitrarily-selected celestial object and fixed with respectto the ground (earth). The present invention also provides aphotographic apparatus that employs this method of automaticallytracking and photographing celestial objects.

According to an aspect of the present invention, a method ofautomatically tracking and photographing a celestial object, isprovided, which moves relative to a photographic apparatus due todiurnal motion so that an image of the celestial object that is formedon an imaging surface of an image sensor via a photographing opticalsystem of the photographic apparatus becomes stationary relative to apredetermined imaging area of the image sensor during a celestial-objectauto-tracking photographing operation, the method including inputtingphotographing azimuth angle information and photographing elevationangle information of the photographic apparatus which is directed towardthe celestial object; calculating preliminary-tracking drive controldata for use in performing a preliminary tracking operation based on thephotographing azimuth angle information and the photographing elevationangle information; obtaining a first preliminary image and a secondpreliminary image which respectively correspond to a commencement pointand a termination point of the preliminary tracking operation;calculating an amount of deviation between a celestial object image inthe first preliminary image and a corresponding celestial object imagein the second preliminary image; calculating, from the amount ofdeviation, actual-tracking drive control data for use in performing anactual tracking operation with the deviation amount cancelled; andperforming the celestial-object auto-tracking photographing operationbased on the actual-tracking drive control data.

It is desirable for the performing of the celestial-object auto-trackingphotographing operation to include performing an exposure operationwhile moving at least one of the predetermined imaging area of the imagesensor and the image of the celestial object that is formed on theimaging surface of the image sensor.

It is desirable for the performing of the celestial-object auto-trackingphotographing operation to include correcting at least one of thephotographing azimuth angle information and the photographing elevationangle information with the deviation amount, and calculatingactual-tracking drive control data for use in moving at least one of thepredetermined imaging area of the image sensor and the image of thecelestial object that is formed on the imaging surface of the imagesensor based on corrected the at least one of the photographing azimuthangle information and the photographing elevation angle information.

It is desirable for the performing of the celestial-object auto-trackingphotographing operation to include correcting the preliminary-trackingdrive control data with the deviation amount to calculateactual-tracking drive control data for use in moving at least one of thepredetermined imaging area of the image sensor and the image of thecelestial object that is formed on the imaging surface of the imagesensor.

It is desirable for the performing of the celestial-object auto-trackingphotographing operation to includes determining whether or not thedeviation amount exceeds a predetermined threshold value; recalculatingthe actual-tracking drive control data for use in performing the actualtracking operation with the deviation amount cancelled in the case wherethe deviation amount is determined as exceeding the predeterminedthreshold value; and substituting the preliminary-tracking drive controldata for the actual-tracking drive control data already calculated inthe case where the deviation amount is determined as one of equal to andless than the predetermined threshold value.

It is desirable for the actual-tracking drive control data to be formoving the image sensor in directions orthogonal to an optical axis ofthe photographing optical system and rotating the image sensor about anaxis parallel to the optical axis while performing an exposureoperation.

It is desirable for the predetermined imaging area of the image sensorto be a trimmed imaging area which is formed by partly trimming anentire imaging area of the image sensor electronically, and for theactual-tracking drive control data to be for moving the trimmed imagingarea in directions orthogonal to an optical axis of the photographingoptical system and rotating the trimmed imaging area about an axisparallel to the optical axis while performing an exposure operation.

It is desirable for the calculating of the deviation amount to includeconverting a position of the celestial object image in the firstpreliminary image to first X-Y coordinates in an X-Y coordinate systemand a position of the corresponding celestial object image in the secondpreliminary image to second X-Y coordinates in the X-Y coordinatesystem, and calculating the deviation amount from a difference betweenthe first X-Y coordinates and the second X-Y coordinates.

It is desirable for the following conditions (V) and (VI) to besatisfied:

ΔX=Xd−Xd cos θ+Yd sin θ  (V)

ΔY=Yd−Xd sin θ−Yd cos θ  (VI)

wherein Δ×designates the amount of deviation between an X-coordinateposition of the celestial object image in the first preliminary imageand an X-coordinate position of the corresponding celestial object imagein the second preliminary image; ΔY designates the amount of deviationbetween a Y-coordinate position of the celestial object image in thefirst preliminary image and a Y-coordinate position of the correspondingcelestial object image in the second preliminary image; Xd designates anamount of deviation of an X-coordinate position of the center point ofthe image that is actually captured by the photographic apparatus withrespect to the position of the center point of the image that iscalculated based on the input photographing azimuth angle informationand the input photographing elevation angle information of thephotographic apparatus; Yd designates an amount of deviation of aY-coordinate position of the center point of the image that is actuallycaptured by the photographic apparatus with respect to the position ofthe center point of the image that is calculated based on the inputphotographing azimuth angle information and the input photographingelevation angle information of the photographic apparatus; and θdesignates a rotational angle of the celestial object image in each ofthe first preliminary image and the second preliminary image with acenter of the imaging surface defined as a rotational center.

It is desirable for the method to include inputting focal lengthinformation of the photographing optical system, and calculating a firstamount of deviation between the photographing azimuth angle informationand the theoretically-correct photographing azimuth angle informationand a second amount of deviation between the photographing elevationangle information and the theoretically-correct photographing elevationangle information using the focal length information, the deviationamount Xd and the deviation amount Yd from the following equations:

Δh=arctan(Yd/f)

ΔA=arccos((cos(arctan(Xd/f))−cos²(hs+arctan(Yd/f)/2))/cos²(hs+arctan(Yd/f)/2))

wherein f designates the focal length information of the photographingoptical system, hs designates the photographing elevation angleinformation, Δh designates the first deviation amount, and ΔA designatesthe second deviation amount.

In an embodiment, a photographic apparatus is provided, whichautomatically tracks and photographs a celestial object which movesrelative to the photographic apparatus due to diurnal motion so that animage of the celestial object that is formed on an imaging surface of animage sensor via a photographing optical system of the photographicapparatus becomes stationary relative to a predetermined imaging area ofthe image sensor during a celestial-object auto-tracking photographingoperation, the camera including an inputter which inputs photographingazimuth angle information and photographing elevation angle informationof the photographic apparatus directed toward the celestial object; animage sensor which obtains a first preliminary image and a secondpreliminary image which respectively correspond to a commencement pointand a termination point of the preliminary tracking operation; and acontroller. The controller calculates preliminary-tracking drive controldata for use in performing a preliminary tracking operation based on thephotographing azimuth angle information and the photographing elevationangle information. The controller calculates an amount of deviationbetween a celestial object image in the first preliminary image and acorresponding celestial object image in the second preliminary image.The controller calculates, from the amount of deviation, actual-trackingdrive control data for use in performing an actual tracking operationwith the deviation amount cancelled. The controller performs thecelestial-object auto-tracking photographing operation based on theactual-tracking drive control data.

According to the method of automatically tracking and photographingcelestial objects, and a photographic apparatus that employs thismethod, according to the present invention, since this method includes:calculating the preliminary-tracking drive control data, which is foruse in performing a preliminary tracking operation, based on thephotographing azimuth angle information and the photographing elevationangle information; obtaining the first preliminary image and the secondpreliminary image, which respectively correspond to the commencementpoint and the termination point of the preliminary tracking operation;calculating the amount of deviation between the celestial object imagein the first preliminary image and the corresponding celestial objectimage in the second preliminary image; calculating, from the amount ofdeviation, the actual-tracking drive control data, which is for use inperforming an actual tracking operation, with the deviation amountcancelled; and performing the celestial-object auto-trackingphotographing operation based on the actual-tracking drive control data,the celestial-object auto-tracking photographing operation with highprecision can be achieved by the calculation of the actual-trackingdrive control data even if the input photographing azimuth angle and theinput photographing elevation angle are low in accuracy, which makes itpossible to capture a still image of a celestial object(s) in a statewhere each celestial object appears stationary even in long exposureastrophotography.

The present disclosure relates to subject matter contained in JapanesePatent Application No. 2010-122909 (filed on May 28, 2010) which isexpressly incorporated herein by reference in its entirety.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described below in detail with referenceto the accompanying drawings in which:

FIG. 1 is a block diagram illustrating main components of an embodimentof a digital camera which is capable of automatically tracking andphotographing celestial objects according to the present invention;

FIG. 2A is a diagram showing an entire image photographed in anastrophotography mode (celestial-object auto tracking photography mode)with errors in the photographing azimuth angle and the photographingelevation angle that are input from an azimuth angle sensor and agravity sensor, respectively;

FIG. 2B is a diagram showing a part of the image shown in FIG. 2A whichincludes an image of a celestial object;

FIG. 3 is a diagram showing an image photographed in thecelestial-object auto tracking photography mode when it is assumed thateach celestial object image merely shifts from one point to another;

FIG. 4 is an explanatory diagram which illustrates a state wherecelestial object images PB and PC have rotated about a celestial objectimage PA;

FIG. 5 is an explanatory diagram which illustrates a state where thecelestial object images PA and PC have rotated about the celestialobject image PB;

FIG. 6 is an explanatory diagram which illustrates movements ofcelestial object images on an imaging surface (picture plane);

FIGS. 7A and 7B are explanatory diagrams for illustrating a technique ofdetermining actual-tracking drive control data (dA/dt, dh/dt, dθ/dt)using declination δ, hour angle H, photographing azimuth angle As andphotographing elevation angle hs with respect to a celestial object andfocal length f during the celestial-object auto-tracking photographingoperation according to the present invention, wherein FIG. 7A is adiagraph illustrating an equatorial coordinate system and FIG. 7B is adiagraph illustrating a spherical triangle of the celestial hemisphereshown in FIG. 7A;

FIG. 8 is a flow chart showing a main process performed when a pictureis taken by the digital camera in either a normal photography mode or anastrophotography mode (celestial-object auto tracking photography mode);

FIG. 9 is a flow chart showing a series of operations performed in thepreliminary photographing operation (step S113) shown in FIG. 8 in thecelestial-object auto-tracking photographing mode; and

FIG. 10 is a flow chart showing a series of operations performed in theactual photographing operation (S115) shown in FIG. 8 in thecelestial-object auto-tracking photographing mode.

DESCRIPTION OF THE PREFERRED EMBODIMENT

An embodiment of a method of automatically tracking and photographingcelestial objects according to the present invention and an embodimentof a digital camera 10 employing this method will be discussedhereinafter. As shown in FIG. 1, the present embodiment of the digitalcamera (photographic apparatus) 10 is provided with a camera body 11 anda photographing lens 101 (that contains a photographing optical systemL). The digital camera 10 is provided, in the camera body 11 behind thephotographing optical system L, with an image sensor 13 serving as animage pickup device. An optical axis Z of the photographing opticalsystem L is orthogonal to an imaging surface (photosensitivesurface/imaging plane) 14 of the image sensor 13. The image sensor 13 ismounted onto an image sensor drive unit (image sensor mover/anti-shakeunit) 15. The image sensor drive unit 15 is provided with a fixed stage,a movable stage which is movable relative to the fixed stage, and anelectromagnetic circuit for moving the movable stage relative to thefixed stage. The image sensor 13 is held by the movable stage. The imagesensor 13 (the movable stage) is controlled and driven to linearly movein desired directions orthogonal to the optical axis Z at a desiredmoving speed and to rotate about an axis parallel to the optical axis Z(instantaneous center at some point in a plane orthogonal to the opticalaxis Z) at a desired rotational speed. This type of image sensor driveunit 15 is known in the art as an anti-shake unit of an image shakecorrector (shake reduction system) incorporated in a camera disclosedin, e.g., Japanese Unexamined Patent Publication No. 2007-25616.

The photographing lens 101 is provided with a diaphragm (adjustablediaphragm) 103 in the photographing optical system L. The f-number(degree of opening/closing the diaphragm 103) is controlled by adiaphragm drive control mechanism 17 provided in the camera body 11. Thephotographing lens 101 of the digital camera 10 is provided with a focallength detector (focal length inputter) 105 for detecting the focallength f of the photographing optical system L.

The digital camera 10 is provided with a CPU 21 which controls theoverall operation of the digital camera 10. The CPU(controller/calculator) 21 drives the image sensor 20 and controls theoperation thereof, and performs a signal processing operation on animage signal of a captured object image to display this image on an LCDmonitor 23, and writes image data of this image into a removable memorycard 25. To detect vibrations applied to the digital camera 10 when theimage sensor drive unit 15 is used as an anti-shake unit, the CPU 21inputs signals sensed by an X-direction gyro sensor GSX, a Y-directiongyro sensor GSY and a rotational-direction gyro sensor GSR.

The camera body 11 is provided with various switches such as a powerswitch 27, a release switch 28 and a setting switch 30. The CPU 21performs controls according to the ON/OFF states of these switches 27,28 and 30. For instance, the CPU 21 turns ON/OFF the power supply from abattery (not shown) upon receipt of an operation signal from the powerswitch 27, and performs a focusing process, a photometering process andan image capturing process (astronomical-image capturing process) uponreceipt of an operation signal from the release switch 28. The settingswitch 30 is for selectively setting various photography modes (exposuremodes) such as a celestial-object auto tracking photography mode and anormal photography mode.

The digital camera 10 is provided in the camera body 11 with a GPS unit31 serving as a latitude information inputter, an azimuth angle sensor33 serving as an azimuth information inputter, and a gravity sensor 35serving as a photographing elevation angle information inputter.Latitude information ε, azimuth information and (photo date information)date/time information (Greenwich Mean Time information) are input to theCPU 21 from the GPS unit 31, and photographing azimuth angle informationAs and photographing elevation angle information hs are input to the CPU21 from an azimuth angle sensor 33 and a gravity sensor 35,respectively. The CPU 21 drives the image sensor drive unit 15 andcontrols operation thereof based on the latitude information ε, which isinput from the GPS unit 31, the photographing azimuth angle informationAs and the photographing elevation angle information hs, which arerespectively input from the azimuth angle sensor 33 and the gravitysensor 35, and focal length information f input from the focal lengthdetector 105. A reference position of the camera body 11 (specificallythe image sensor 13 thereof) is, e.g., a position (posture) in which thelong-side direction of the image sensor 13 is coincident with thehorizontal direction (X-direction), and this reference position isdefined by an X-Y coordinate system the X-axis (X-direction) and Y-axis(Y-direction) of which correspond to the long-side direction and theshort-side direction of the rectangular image sensor 13, respectively.

Each of the above described GPS unit 31, azimuth angle sensor 33 andgravity sensor 35 can be not only a built-in type that is incorporatedinto the camera body 11 but an external type that is attached to thecamera body. Specifically, it is possible to install such externaldevices to an accessory shoe or a bracket attached to the base plate ofthe camera body 11, and output signals from the external devices can beinput to the CPU 21 via electrical contacts on the accessory shoe or aconnector such as a USB connector (socket/plug). Date/time informationthat is input to the CPU 21 can be obtained from a built-in clock, andlatitude information ε can be manually input to the CPU 21 by the uservia the setting switch 30.

To photograph a still image of a celestial object(s) that moves relativeto the digital camera 10 due to diurnal motion, the digital camera 10performs an auto-tracking photographing operation while moving at leastone of a predetermined imaging area of the image sensor 13 (the imagingsurface 14) and an image of the celestial object that is formed on theimaging surface 14 of the image sensor 13 relative to the digital camera10 so that the image of the celestial object, which is formed on theimaging surface 14 via the photographing optical system L of the digitalcamera 10, becomes stationary relative to the predetermined imaging areaof the image sensor during the auto-tracking photographing operation.Operations of the digital camera 10 will be discussed in further detailhereinafter.

With the digital camera 10 directed toward an arbitrarily-selectedcelestial object, the azimuth angle sensor 33 actually measures(detects) the photographing azimuth angle As of the digital camera 10and the gravity sensor 35 actually measures (detects) the photographingelevation angle hs. The azimuth angle sensor 33 and the gravity sensor35 input the actually measured photographing azimuth angle As andphotographing elevation angle hs to the CPU 21.

Based on the photographing azimuth angle As and the photographingelevation angle hs that are input from the azimuth angle sensor 33 andthe gravity sensor 35, respectively, the CPU 21 calculatespreliminary-tracking drive control data (dAs/dt, dhs/dt, dθ/dt) for usein performing a preliminary tracking operation. Based on thispreliminary-tracking drive control data (dAs/dt, dhs/dt, dθ/dt), the CPU21 performs an exposure operation while performing the aforementionedpreliminary tracking operation (in which the CPU 21 linearly moves theimage sensor 13 and rotates the image sensor 13 about an axis parallelto the optical axis LO) to obtain a first preliminary image and a secondpreliminary image which correspond to the commencement point and thetermination point of the preliminary tracking operation, respectively.

It is possible to obtain the first preliminary image and the secondpreliminary image by making an exposure with a short exposure time ateach of the commencement point and the termination point of thepreliminary tracking operation, or by making an exposure with a longexposure time during the preliminary tracking operation and extracting aphotographic image at each of the commencement point and the terminationpoint (i.e., both ends) of the preliminary tracking operation.

The CPU 21 calculates the amount of deviation (ΔX) and the amount ofdeviation (ΔY) of the image of a celestial object in the obtained firstpreliminary image from the image of the corresponding celestial objectin the obtained second preliminary image in the horizontal direction(X-direction) and the vertical direction (Y-direction), respectively,and calculates actual-tracking drive control data (dA/dt, dh/dt, dθ/dt)for use in performing an actual tracking operation with the deviationamounts (ΔX, ΔY) canceled. Two methods (first and second methods) ofcalculating the actual-tracking drive control data (dA/dt, dh/dt, dθ/dt)which will be discussed hereinafter are available.

According to the first method, from the calculated deviation amounts(ΔX, ΔY), the photographing azimuth angle information As that is inputfrom the azimuth angle sensor 33 and the photographing elevation angleinformation hs that is input from the gravity sensor 35 are corrected byan error (deviation amount) ΔA in the photographing azimuth angle As andan error (deviation amount) Δh in the photographing elevation angleinformation hs to obtain a theoretically-correct photographing azimuthangle information A (i.e., As+ΔA) and a theoretically-correctphotographing elevation angle information h (i.e., hs+Δh), respectively.Thereafter, based on the theoretically-correct photographing azimuthangle information A and the theoretically-correct photographingelevation angle information h, the CPU 21 calculates the actual-trackingdrive control data (dA/dt, dh/dt, dθ/dt). If one of the azimuth anglesensor 33 and the gravity sensor 35 is a high-precision sensor (if oneof the photographing azimuth angle information As and the photographingelevation angle information hs is close to the theoretically-correctphotographing azimuth angle information A or the theoretically-correctphotographing elevation angle information h), it is possible to onlycorrect the error caused by the other.

According to the second method, from the calculated deviation amounts(ΔX, ΔY), the preliminary-tracking drive control data (dAs/dt, dhs/dt,dθ/dt) is directly corrected to calculate the actual-tracking drivecontrol data (dA/dt, dh/dt, dθ/dt).

If the photographing azimuth angle As and the photographing elevationangle hs that are respectively input from the azimuth angle sensor 33and the gravity sensor 35 are accurate (high in accuracy), there is noneed to calculate the actual-tracking drive control data (dA/dt, dh/dt,dθ/dt); namely, a high-precision celestial-object auto-trackingphotographing operation can be performed using the preliminary-trackingdrive control data (dAs/dt, dhs/dt, dθ/dt).

Accordingly, it is desirable for the CPU 21 to determine whether or notat least one of the calculated deviation amount ΔX and the calculateddeviation amount ΔY exceeds a corresponding predetermined thresholdvalue, and to recalculate the preliminary-tracking drive control data(dAs/dt, dhs/dt, dθ/dt) if either the calculated deviation amount ΔX andthe calculated deviation amount ΔY exceeds the corresponding thresholdvalue, or to substitute the preliminary-tracking drive control data(dAs/dt, dhs/dt, dθ/dt) for the actual-tracking drive control data(dA/dt, dh/dt, dθ/dt) if neither of the calculated deviation amount ΔXand the calculated deviation amount ΔY exceeds the correspondingthreshold value. According to this control, the burden on the CPU 21 canbe reduced by omitting redundant computations.

Accordingly, the CPU 21 performs the celestial-object auto-trackingphotographing operation (actual photographing operation) whileperforming the actual tracking operation (in which the CPU 21 linearlymoves the image sensor 13 and rotates the image sensor 13 about an axisparallel to the optical axis LO) based on the calculated actual-trackingdrive control data (dA/dt, dh/dt, dθ/dt).

A principle which enables the celestial-object auto trackingphotographing operation to be performed by linear movement (linearshift) of the imaging surface (imaging area) 14 in directions orthogonalto the optical axis LO and rotational movement of the imaging surface(imaging area) 14 about an axis parallel to the optical axis LO will behereinafter discussed with reference to FIGS. 3 through 5. In thefollowing descriptions, a direction orthogonal to the optical axis LOand parallel to the long-side direction of the rectangular imagingsurface 14 of the image sensor 13 in its initial position is defined asX-direction (direction parallel to the X-axis), a direction orthogonalto the optical axis LO and parallel to the short-side direction of therectangular imaging surface 14 of the image sensor 13 in its initialposition is defined as Y-direction (direction parallel to the Y-axis),and a direction parallel to the optical axis LO is defined asZ-direction (direction parallel to a Z-axis orthogonal to both theX-axis and the Y-axis). In addition, an orthogonal coordinate system ina plane orthogonal to the optical axis LO is defined as theaforementioned X-Y coordinate system. The image sensor drive unit 15 isprovided with image sensor (13) mechanical movement limits Lx, Ly in theX-direction and the Y-direction from the initial position thereof, andis provided with an image sensor (13) mechanical rotation limit Le aboutthe Z-axis that extends in the optical axis LO direction (Z-direction).

FIG. 3 shows a state where it is assumed that the image sensor 13 isdriven only to shift in the X-direction and the Y-direction (i.e. not torotate about an axis parallel to the optical axis LO) by control of theCPU 21. In the linear shift control in the X and Y directions, in whichno rotation movement control is performed, celestial object images S1,S2, S3, S4 and S5 formed on the imaging surface 14 integrally move inthe X and Y directions without changing the relative positiontherebetween. Accordingly, if the image sensor 13 is driven to shift byan amount in the X and Y directions which corresponds to the shiftamount of the celestial object images S1, S2, S3, S4 and S5 in the X andY directions, a high-precision celestial-object auto-trackingphotographing operation can be, in theory, performed. Namely, even if acalculated (arithmetic) image center point which is determined bycalculation from the photographing azimuth angle information As and thephotographing elevation angle information hs, which are respectivelyinput from the azimuth angle sensor 33 and the gravity sensor 35,deviates from the actual photograph direction of the digital camera 10,the shift control in the X and Y directions is not adversely effected.Accordingly, the deviation between the calculated image center point andthe actual photograph direction of the digital camera 10 only influencesthe rotation control of the image sensor 13.

However, celestial object images PA, PB and PC formed on the imagingsurface 14 integrally rotate about the center (image center) of theimaging surface 14 as shown in FIGS. 4 and 5 if it is assumed that thecenter of the imaging surface 14, which captures the celestial objectimages PA, PB and PC, corresponds to the aforementioned calculated imagecenter point.

In FIG. 4, if the celestial object image PA is deemed to be positionedat the calculated image center point, each of the celestial objectimages PB and PC has rotated about the celestial object image PA in thecounterclockwise direction with respect to FIG. 4 by an angle ofrotation θ. In this case, the calculated image center point, where thecelestial objet image PA is positioned, is defined as an origin point ofthe X-Y coordinate system. If the point PB (Xb, Yb) is rotated about theorigin point (celestial image) PA by the angle of rotation θ and if thepoint PB after it has rotated about the origin point PA the angle ofrotation θ is defined as a point PB1 (Xb1, Yb1), the coordinates of thepoint PB1 can be expressed by the following equation (I):

PB1(Xb1,Yb1)=(Xb cos θ−Yb cos θ,Xb sin θ+Yb cos θ)  (I)

In FIG. 5, each of the celestial object images PA and PC has rotatedabout the celestial object image PB in the counterclockwise directionwith respect to FIG. 5 by the angle of rotation θ since the celestialobject image PB is positioned at the calculated image center position.Since the point PA has rotated about the point PB (Xb, Yb) by the angleof rotation θ to move to a point PA2 (Xa2, Ya2), the coordinates of thepoint PA2 (Xa2, Ya2) can be expressed by the following equation (II):

PA2(Xa2,Ya2)(Xb−Xb cos θ+Yb sin θ,Yb−Xb sin θ−Yb cos θ)  (II)

Accordingly, the amount of movement of the point PA from the initialposition thereof shown in FIG. 5 with a rotational center of the imagingsurface 14 defined as the point PB and the amount of movement of thepoint PB from the initial position shown in FIG. 4 with a rotationalcenter of the imaging surface 14 defined as the point PA can beexpressed by the following equations (III) and (IV), respectively:

$\begin{matrix}\begin{matrix}{{{Movement}\mspace{14mu} {amount}\mspace{14mu} {of}\mspace{14mu} {point}\mspace{14mu} {PA}} = \left( {{{{Xa}\; 2} - {Xa}},{{{Ya}\; 2} - {Ya}}} \right)} \\{= \begin{pmatrix}{{{Xb} - {{Xb}\; \cos \; \theta} + {{Yb}\; \sin \; \theta}},} \\{{Yb} - {{Xb}\; \sin \; \theta} - {{Yb}\; \cos \; \theta}}\end{pmatrix}}\end{matrix} & ({III}) \\\begin{matrix}{{{Movement}\mspace{14mu} {amount}\mspace{14mu} {of}\mspace{14mu} {point}\mspace{14mu} {PB}} = \left( {{{Xb} - {{Xb}\; 1}},{{Yb} - {{Yb}\; 1}}} \right)} \\{= \begin{pmatrix}{{{Xb} - {{Xb}\; \cos \; \theta} + {{Yb}\; \sin \; \theta}},} \\{{Yb} - {{Xb}\; \sin \; \theta} - {{Yb}\; \cos \; \theta}}\end{pmatrix}}\end{matrix} & ({IV})\end{matrix}$

It can be understood from these equations that the amount of movement ofthe point PA from the initial position thereof and the amount ofmovement of the point PB from the initial position thereof are mutuallyidentical. Likewise, the amount of movement of the point PC from theinitial position is identical to that of the point PB in FIG. 4 and theamount of movement of the point PC from the initial position isidentical to that of the point PA in FIG. 5. According to the above,when a celestial object image rotates by the rotational angle θ in theimaging surface 14, all points in the imaging surface 14 integrally movein a linear manner as shown in FIG. 6 if the image sensor 13 (theimaging surface 14) is rotated by the same rotational angle.Additionally, if the image sensor 13 (the imaging surface 14) is drivento move in the X and Y directions by an amount of movement correspondingto the linear movement amount, a high-precision celestial-objectauto-tracking photographing operation can be performed. This linearmovement amount is determined by rotational center deviation amounts(Xd, Yd) which will be discussed later and the rotational angle θ.

In the present embodiment, the CPU 21 calculates thepreliminary-tracking drive control data (dAs/dt, dhs/dt, dθ/dt) for theimage sensor 13 from the photographing azimuth angle As and thephotographing elevation angle hs that are input from the azimuth anglesensor 33 and the gravity sensor 35, respectively. “dAs/dt”, “dhs/dt”,“dθ/dt” designate an azimuth-angle-direction driving speed, anelevation-angle-direction driving speed and a rotational driving speed,respectively. The azimuth-angle-direction driving speed dAs/dt is datafor moving the image sensor 13 in the X-direction, theelevation-angle-direction driving speed dhs/dt is data for moving theimage sensor 13 in the Y-direction, and the rotational driving speeddθ/dt is data for rotating the image sensor 13 about a center thereof.

A manner of calculating the preliminary-tracking drive control data(dAs/dt, dhs/dt, dθ/dt) will be hereinafter discussed with reference toa celestial hemisphere shown in FIG. 7A and a spherical triangle shownin FIG. 7B.

In the celestial diagrams shown in FIGS. 7A and 7B, P, Z, N, S, ε, As,hs, H and δ designate north celestial pole (NCP), zenith, true north,target celestial object, latitude at a photographic site, photographingazimuth angle (photographing azimuth angle input from the azimuth anglesensor 33), photographing elevation angle (photographing elevation angleinput from the gravity sensor 35), hour angle of the target celestialobject and declination of the target celestial object, respectively. Theazimuth-angle-direction driving speed dAs/dt, theelevation-angle-direction driving speed dhs/dt and the rotationaldriving speed dθ/dt can be determined in a manner which will bediscussed hereinafter.

In regard to the celestial diagrams shown in FIGS. 7A and 7B, thefollowing equations are obtained:

sin hs=sin ε×sin δ+cos ε×cos δ×cos H  (a)

tan As=sin H/(cos ε×tan δ−sin ε×cos H)  (b)

tan θ=sin H/(tan ε×cos δ−sin δ×cos H)  (c)

dz/dt=cos δ×sin θ  (d)

(z=90−hs)

dAs/dt=cos δ×cos θ/cos hs  (e)

dθ/dt=−cos ε×cos As/cos hs  (f)

The values to be obtained are: the declination δ of the target celestialobject, the hour angle H of the target celestial object, theazimuth-angle-direction driving speed dAs/dt, theelevation-angle-direction driving speed dhs/dt and the rotationaldriving speed dθ/dt when the latitude c, the photographing azimuth angleAs and the photographing elevation angle hs. These values are obtainedby assigning the latitude c, the photographing azimuth angle As and thephotographing elevation angle hs to equations (g) through (k) below:

sin δ=sin hs×sin ε+cos hs×cos ε×cos As  (g)

tan H=sin As/(cos ε×tan hs−sin ε×cos As)  (h)

dAs/dt=sin ε−cos ε×tan hs×cos As  (i)

dhs/dt=−sin As×cos ε  (j)

dθ/dt=−cos As×cos ε/cos hs  (k)

FIGS. 2A and 2B show the results obtained when the digital camera 10performs a short-time exposure operation at each of the commencementpoint and the termination point of the preliminary tracking operationwhile performing the preliminary tracking operation using thepreliminary-tracking drive control data (dAs/dt, dhs/dt, dθ/dt). In thispreliminary tracking operation, the preliminary photographing operationis performed with more than one short-time exposure operation, not witha long-time exposure operation, so that celestial objects arephotographed as dots. More specifically, in a single preliminaryphotographing operation, a first exposure (short-time exposureoperation) is performed at the commencement of the preliminary trackingoperation and a second exposure (short-time exposure operation) isperformed at the termination of the same preliminary tracking operation.Because each of the first and second exposures is short in exposuretime, it is desirable that the diaphragm 103 be fully open to increasethe amount of exposure or the ISO sensitivity be increased as much aspossible during each of the first and second exposures. An exposure witha short exposure time can be performed more than twice in a singlepreliminary tracking operation.

In the preliminary image shown in FIGS. 2A and 2B that is obtained bythe preliminary photographing operation, a deviation amount (trackingerror amount) ΔX in the X-direction (horizontal direction with respectto FIGS. 2A and 2B) and a deviation amount (tracking error amount) ΔY inthe Y-direction (vertical direction with respect to FIGS. 2A and 2B) canbe seen in each of the celestial object images S1 through S5. Namely, asshown in FIGS. 2A and 2B, due to the deviation amounts ΔX and ΔY,celestial object images S1′ through S5′ (which are the same celestialobjects as those of the celestial object images S1 through S5,respectively) that are formed on the imaging surface 14 by theaforementioned first exposure that is performed at the commencement ofthe preliminary tracking operation do not match the celestial objectimages S1 through S5, respectively, that are formed on the imagingsurface 14 by the aforementioned second exposure that is performed atthe termination of the preliminary tracking operation. These deviationamounts ΔX and ΔY are caused by a deviation of the rotational centerthat is caused by a difference between the measured photographingazimuth angle As and photographing elevation angle hs and the actualorientation of the digital camera 10 due to errors such as thoseoccurring in the measurement by the azimuth angle sensor 33 and thegravity sensor 35. If deviation amounts (Xd, Yd) of this rotationalcenter can be determined, the celestial-object auto-trackingphotographing operation can be performed with extremely high precisionby correcting the photographing azimuth angle As and the photographingelevation angle hs with the errors ΔA and Ah and calculating theactual-tracking drive control data (dA/dt, dh/dt, dθ/dt) from thecorrected (theoretically correct) photographing azimuth angle A (i.e.,As+ΔA) and the corrected (theoretically correct) photographing elevationangle h (i.e., hs+Δh).

A manner of calculating the rotational center deviation amounts Xd andYd from the deviation amounts ΔX and ΔY, respectively, which areobtained by the preliminary photographing operation, will be discussedhereinafter.

One celestial object is arbitrarily selected from the first preliminaryimage and the second preliminary image, which are obtained by thepreliminary photographing operation, and the deviation amounts (movingamounts) ΔX and ΔY of this one celestial object in the X and Ydirections are determined. In addition, the rotational angle θ of thisone celestial object is calculated from the first preliminary image andthe second preliminary image. Since those moving amounts ΔX and ΔYcorrespond to those of the point PA of the aforementioned equation (III)or those of the point PB of the aforementioned equation (IV), thefollowing equations (V) and (VI) are obtained:

ΔX=Xd−Xd cos θ+Yd sin θ  (V)

ΔY=Yd−Xd sin θ−Yd cos θ  (VI)

wherein ΔX represents the amount of deviation in the X-coordinate of theimage of the arbitrarily selected celestial object in the firstpreliminary image from the image of the corresponding celestial objectin the second preliminary image;

ΔY represents the amount of deviation in the Y-coordinate of the imageof the arbitrarily selected celestial object in the first preliminaryimage from the image of the corresponding celestial object in the secondpreliminary image;

Xd designates the rotational center deviation amount of the X-coordinateposition (the amount of deviation of the X-coordinate position of thecenter point of the image of that is actually captured by the camera(photographic apparatus) 10 with respect to the position of the centerpoint of the image that is calculated based on the input photographingazimuth angle information A and the input photographing elevation angleinformation h of the digital camera (photographic apparatus) 10);

Yd designates the rotational center deviation amount of the Y-coordinateposition (the amount of deviation of the Y-coordinate position of thecenter point of the image that is actually captured by the camera(photographic apparatus) 10 with respect to the position of the centerpoint of the image that is calculated based on the input photographingazimuth angle information A and the input photographing elevation angleinformation h of the digital camera (photographic apparatus) 10); and

θ represents the rotational angle of the arbitrarily selected celestialobject image in each of the first preliminary image and the secondpreliminary image with the center of the imaging surface defined as arotational center.

If the aforementioned equations (V) and (VI) are solved with respect toXd and Yd, the following equations are obtained:

Xd=ΔX/2−ΔY sin θ/(2(1−cos θ))

Yd=Δ×sin θ/(2(1−cos θ))+ΔY/2

As described above, the rotational center deviation amounts Xd and Ydcan be calculated from the deviation amounts ΔX and ΔY and therotational angle θ that are obtained from the first preliminary imageand the second preliminary image. Consequently, if the tracking controlis performed with the rotational center shifted by the rotational centerdeviation amounts Xd and Yd and with the X-direction moving amount ΔX,the Y-direction moving amount ΔY and the rotational angle θ of the imagesensor 13 (and hence, image that is actually captured by thephotographic apparatus) remaining unchanged, a precise trackingastrophotography with (substantially) no error becomes possible.

In addition, the photographing azimuth angle As and the photographingelevation angle hs can be corrected with the rotational center for usein control remaining unchanged as a sensor center (calculated imagecenter point). From the above calculated rotational center deviationamounts Xd and Yd, the deviation amount ΔA in the photographing azimuthangle As and the deviation amount Δh in the photographing elevationangle information hs can be expressed as follows:

Δh=arctan(Yd/f)

ΔA=arccos((cos(arctan(Xd/f))−cos²(h+arctan(Yd/f)/2))/cos²(h+arctan(Yd/f)/2))

The deviation amounts ΔA and Δh are correction amounts for thephotographing azimuth angle As and the photographing elevation angleinformation hs, which are obtained by the azimuth angle sensor 33 andthe gravity sensor 35, respectively. With this, the accuratephotographing azimuth angle A (i.e., As+ΔA) and the accuratephotographing elevation angle h (i.e., hs+Δh) can be calculated bycorrecting the photographing azimuth angle As and the photographingelevation angle information hs, which are respectively obtained by theazimuth angle sensor 33 and the gravity sensor 35 and each of which mayinclude an error, with the deviation amounts ΔA and Δh.

The fact that the aforementioned equations (g), (h), (i), (j) and (k)are valid will be discussed (proven) hereinafter.

In a spherical triangle ΔZPS on the celestial hemisphere shown in FIG.7A, the following three equations are valid according to the sphericallaw of cosines.

sin(90−h)×sin θ=sin(90−ε)×sin H

sin(90−h)×cos θ=sin(90−δ)×cos(90−ε)cos(90−δ)×sin(90−ε)×cos H

cos(90−h)=cos(90−ε)×cos(90−δ)+sin(90−ε)×sin(90−δ)×cos H

If each of the these three equations is modified, the followingequations (1), (2) and (3) are obtained.

cos h×sin θ=cos ε×sin H  (1)

cos h×cos θ=cos δ×sin ε−sin δ×cos ε×cos H  (2)

sin h=sin ε×sin δ+cos ε×cos δ×cos H  (3)

The following equation (4) is obtained from the aforementioned equations(1) and (2). This equation (4) is equivalent to the aforementionedequation (c).

$\begin{matrix}\begin{matrix}{{\tan \; \theta} = {\cos \; ɛ \times \sin \; {H/\left( {{\cos \; \delta \times \sin \; ɛ} - {\sin \; \delta \times \cos \; ɛ \times \cos \; H}} \right)}}} \\{= {\sin \; {H/\left( {{\tan \; ɛ \times \cos \; \delta} - {\sin \; \delta \times \cos \; H}} \right)}}}\end{matrix} & (4)\end{matrix}$

If both sides of each of equations (1) and (2) are differentiated withrespect to t, the following equations (5) and (6) are obtained.

−sin h×sin θ×dh/dt+cos h×cos θ×dθ/dt=cos ε×cos H  (5)

−sin h×cos θ×dh/dt−cos h×sin θ×dθ/dt=cos ε×sin δ×sin H  (6)

If these equations (5) and (6) are solved in terms of dh/dt and dθ/dt,the following equation is obtained:

−sin h×sin θ×cos θ×dh/dt+cos h×cos θ×cos θ×dθ/dt=cos θ×cos ε×cos H

This equation is equal to the right side of equation (5) multiplied bycos θ.

−sin h×sin θ×cos θ×dh/dt−cos h×sin θ×sin θ×dθ/dt=sin θ×cos ε×sin δ×sin H

This equation is equal to the right side of equation (6) multiplied bysin θ. If the right side and the left side of the latter equation of theaforementioned two equations are respectively subtracted from the rightside and the left side of the former equation, the following equationsare obtained:

cos h×dθ/dt×(cos²θ+sin²θ)=cos θ×cos ε×cos H−cos θ×cos ε×sin δ×sin H

cos h×dθ/dt=(cos θ×cos H−sin θ×sin δ×sin H)×cos ε

Accordingly, dθ/dt is expressed by the following equation (7):

dθ/dt=(cos θ×cos H−sin θ×sin δ×sin H)×cos ε/cos h  (7)

In addition, the following two equations hold true:

−sin h×sin θ×sin θ×dh/dt+cos h×sin θ×cos θ×dθ/dt=sin θ×cos ε×cos H

−sin h×cos θ×cos θ×dh/dt−cos h×sin θ×cos=θ×dθ/dt=cos θ×cos ε×sin δ×sin H

The former equation is equivalent to the right side of equation (5)multiplied by sin θ, and the latter equation equivalent to the rightside of equation (6) multiplied by cos θ. Therefore, if the right sideand the left side of the latter equation of the aforementioned twoequations are respectively added to the right side and the left side ofthe former equation, the following equations are obtained:

−sin h×dh/dt×(sin²θ+cos² θ)=sin θ×cos ε×cos H+cos θ×cos ε×sin δ×sin H

−sin h×dh/dt=(sin θ×cos H+cos θ×sin δ×sin H)×cos ε

Accordingly, dh/dt is expressed by the following equation (8):

dh/dt=−(sin θ×cos H+cos θ×sin δ×sin H)×cos ε/sin h  (8)

In the spherical triangle ΔZPS, the following two equations hold trueaccording to the spherical law of cosines:

sin A×cos(90−h)=sin θ×cos H+cos θ×cos(90−δ)×sin H

cos A=cos θ×cos H−sin θ×cos(90−δ)×sin H

These two equations can be modified to obtain the following equations(9) and (10):

sin A×sin h=sin θ×cos H+cos θ×sin δ×sin H  (9)

cos A=−cos θ×cos H+sin θ×sin δ×sin H  (10)

If equations (10) and (9) are substituted into equations (7) and (8),respectively, the following equations (11) and (12) that arerespectively identical to the aforementioned equations (k) and (j) areobtained.

dθ/dt=−cos A×cos ε/cos h  (11)

dh/dt=−sin A×cos ε  (12)

In the spherical triangle ΔZPS, the following equation is obtained:

sin(90−h)×(−cos A)=sin(90−ε)×cos(90−δ)−cos(90−ε)×sin(90−δ)×cos H

This equation can be modified to obtain the following equation:

−cos A=(sin ε×cos θ×cos H−cos ε×sin δ)/cos h

If this equation is substituted into equation (11), the followingequation (13) is obtained.

dθ/dt=(sin ε×cos δ×cos H−cos ε×sin δ)×cos ε/cos² h  (13)

In the spherical triangle ΔZPS, the following equation is obtained:

cos(90−δ)=cos(90−ε)×cos(90−+sin(90−ε)×sin(90−h)×(−cos A)

This equation can be modified to obtain the following equation (14):

sin δ=sin ε×sin h+cos ε×cos h×cos A(g)  (14)

Consequently, the aforementioned equation (g) is obtained.

Additionally, in the spherical triangle ΔZPS, the following equation isobtained:

cos(90−h)=cos(90−δ)×cos(90−ε)+sin(90−δ)×sin(90−ε)×cos H

If the following equation “sin(90−δ)=sin(90−h)×sin A/sin H” issubstituted into this equation, the following equation is obtained:

cos(90−h)=cos(90−δ)×cos(90−ε)sin(90−h)×sin A×sin(90−ε)×cos H/sin H

By modifying this equation, the following equation is obtained:

sin h=sin δ×sin ε+cos h×sin A×cos ε/tan H

If equation (14) is substituted into this equation, the followingequations are obtained:

sin h=sin h×sin² ε+cos ε×sin ε×cos h×cos A+cos h×sin A×cos ε/tan H

cos h×sin A×cos ε/tan H=sin h×(1−sin² E)−cos ε×sin ε×cos h×cos A

tan H=cos h×sin A×cos ε/(sin h×cos² ε+cos ε×sin ε×cos h×cos A)

tan H=sin A/(cos ε×tan h−sin ε×cos A)  (h)

Consequently, the aforementioned equation (h) is obtained.

By modifying equation (a), the following equation (15) is obtained:

sin δ=(sin h−cos ε×cos δ×cos H)/sin ε  (15)

In the spherical triangle ΔZPS, the following equation is obtained:

sin(90−δ)×cos H=cos(90−h)×sin(90−ε)+sin(90−h)×cos(90−ε)×cos A

Therefore, the following equation (16) is obtained:

cos δ×cos H=sin h×cos ε−cos h×sin ε×cos A  (16)

If equation (16) is substituted into equation (15), the followingequations are obtained, thus being equal to equations (14) or (g).

sin δ=(sin h−sin h×cos² ε+cos h×sin ε×cos ε×cos A)/sin ε

sin δ=(sin h×sin² ε+cos h×sin ε×cos ε×cos A)/sin ε

sin δ=sin h×sin ε+cos h×cos ε×cos A

Equation (b) is modified as follows:

−cos A/sin A=sin ε/tan H−cos ε×tan δ/sin H

tan H=sin ε/(−cos A/sin A+cos ε×tan δ/sin H)

This equation is modified as follows by substituting an equation “sinH=sin A×sin(90−h)/sin(90−δ)=sin A×cos h/cos h” into the aforementionedequation.

tan H=sin ε/(−cos A/sin A+cos ε×tan δ×cos δ/sin A×cos h)

tan H=sin ε/(−cos A/sin A+cos ε×sin δ/(sin A×cos h))

tan H=sin ε×sin A/(−cos A+cos ε×sin δ/cos h)

If this equation is modified by substitution of equation (14) thereinto,the following equations are obtained:

tan H=sin ε×sin A/(−cos A+(cos ε×sin h×sin cos² ε×cos h×cos A)/cos h)

tan H=sin ε×sin A/(−cos A+cos ε×sin ε×tan h+cos² ε×cos A)

tan H=sin ε×sin A/(−cos A×sin² ε+cos ε×sin ε×tan h)

tan H=sin A/(−cos A×sin F+cos ε×tan h)  (h)

Consequently, the resultant equation is coincident with theaforementioned equation (h).

In the spherical triangle ΔZPS, the following equations are obtained:

sin(90−δ)×cos θ=cos(90−ε)×sin(90−h)+sin(90−ε)×cos(90−h)×cos A

cos δ×cos θ=sin ε×cos h−cos ε×sin h×cos A

If this equation is substituted into equation (e), the followingequations are obtained:

dA/dt=(sin ε×cos h−cos ε×sin h×cos A)/cos h

dA/dt=sin ε−cos ε×tan h×cos A  (i)

Consequently, the aforementioned (i) is obtained.

Equation (g) is modified as follows:

sin h×sin ε=−cos h×cos ε×cos A+sin δ

This equation is differentiated with respect to t. However, it is deemedthat the latitude ε and the declination δ at a photographic site areconstant.

cos h×sin ε×dh/dt=cos ε×sin h×cos A×dh/dt−cos ε×cos h×sin A×dA/dt

dA/dt=−(cos h×sin ε−cos ε×sin h×cos A)×dh/dt/(cos ε×cos h×sin A)

If equation (j) is substituted into this equation, the followingequations are obtained:

dA/dt=(cos h×sin−cos ε×sin h×cos A)×sin A×cos ε/(cos ε×cos h×sin A)

dA/dt=sin ε−cos ε×tan h×cos A  (i)

thus coinciding with the aforementioned equation (i).

According to the above described principle, the preliminary-trackingdrive control data (dAs/dt, dhs/dt, dθ/dt) for performing thepreliminary tracking operation can be calculated from the photographingazimuth angle As and the photographing elevation angle hs according tothe aforementioned equations (i), (j) and (k). In addition, theactual-tracking drive control data (dA/dt, dh/dt, dθ/dt) for use inperforming an actual tracking operation can be calculated from thecorrected photographing azimuth angle A (i.e., As+ΔA) and the correctedphotographing elevation angle h (i.e., hs+Δh) according to theaforementioned equations (i), (j) and (k).

Astrophotography (celestial-object auto tracking photography) using thedigital camera 10 will be hereinafter discussed with reference to theflow charts shown in FIGS. 8 through 10. As shown in FIG. 8, upon therelease switch 28 being turned ON with the power switch 27 ON, a normalphotography (normal exposure operation) is performed if the digitalcamera 10 is in a normal photography mode (not the celestial-object autotracking photography mode) that is set by turning OFF the setting switch30 (step S101, NO at step S103, YES at step S105, NO at step S107, andstep S109). Control ends upon the power switch 27 being turned OFF (YESat step S103, END). No photographing operation is performed unless therelease switch 28 is turned ON (NO at step S105).

In a state where the power switch 27 is in the ON state and the digitalcamera 10 is in the celestial-object auto tracking photography mode thatis set by the setting switch 30 (S101, NO at step S103), thecelestial-object auto-tracking photographing operation according to thepresent embodiment is performed upon the release switch 28 being turnedON with a target celestial object(s) or star(s) captured on the imagesensor 13 (YES at step S105, YES at step 107).

If astrophotography is carried out with the digital camera 10 not in anastrophotography correction mode (the celestial-object auto trackingphotography mode in which the preliminary-tracking drive control dataand the actual-tracking drive control data are used) (NO at step S111,S115), since the image sensor 13 (the imaging surface 14) remainsstationary at the initial position thereof, the resultant images thereofbecome linearly or curvilinearly elongated light trial images due todiurnal motion of the celestial objects.

On the other hand, if astrophotography is carried out with the digitalcamera 10 in the astrophotography correction mode (the celestial-objectauto tracking photography mode in which the preliminary-tracking drivecontrol data and the actual-tracking drive control data are used) (YESat step S111), a preliminary photographing operation is performedaccording to the preliminary-tracking drive control data (step S113) andthereafter the actual photographing operation (the celestial-objectauto-tracking photographing operation) is performed according to theactual-tracking drive control data (step S115).

[Preliminary Photographing Operation]

The preliminary photographing operation performed at step S113 in whichthe preliminary-tracking drive control data is calculated will behereinafter discussed in detail with reference to the flow chart shownin FIG. 9.

In the preliminary photographing operation, first the CPU 21 inputs thelatitude information ε from the GPS unit 31, inputs the photographingazimuth angle As and the photographing elevation angle hs from theazimuth angle sensor 33 and the gravity sensor 35, respectively, andinputs the focal length information f from the focal length detector 105(step S201).

Subsequently, the CPU 21 calculates the preliminary-tracking drivecontrol data (dAs/dt, dhs/dt, dθ/dt) for use in performing thepreliminary tracking operation based on the latitude information ε, thephotographing azimuth angle As, the photographing elevation angle hs andthe focal length information f that are input at step S201 (step S203).

Subsequently, upon obtaining the first preliminary image (step S204),the CPU 21 performs the preliminary tracking operation (step S205) by(linearly and rotationally) moving the image sensor 13 based on thecalculated preliminary-tracking drive control data (dAs/dt, dhs/dt,dθ/dt). This preliminary tracking operation (step S205) is to the sameas the tracking operation of a later-described actual photographingoperation (steps S305 through S319) shown in FIG. 10 except that thepreliminary-tracking drive control data (dAs/dt, dhs/dt, dθ/dt) issubstituted for the actual-tracking drive control data (dA/dt, dh/dt,dθ/dt). Namely, similar to the actual auto-tracking photographingoperation (the celestial-object auto-tracking photographing operation),the CPU 21 controls the image sensor 13 to linearly and rotationallymove according to the calculated preliminary-tracking drive control data(dAs/dt, dhs/dt, dθ/dt) until a lapse of a set exposure time T. Upon theset exposure time T lapsing, the CPU obtains the second preliminaryimage (step S206). Upon completion of the preliminary tracking operation(step S205), the CPU 21 brings the image sensor 13 back to the initialposition thereof. Note that during this preliminary tracking operation,an exposure can be continuously performed during the preliminarytracking operation (step S205) from when the first preliminary image isobtained (step S204) until when the second preliminary image is obtained(step S206) so as to obtain a preliminary-tracking photographic image.In this case, the first preliminary image and the second preliminaryimage can be extracted from this preliminary-tracking photographicimage.

Subsequently, the CPU 21 converts the position of one of the celestialobject images contained in the first preliminary image to the X-Ycoordinates in the X-Y coordinate system and converts the position ofthe corresponding (same) celestial object image contained in the secondpreliminary image to the X-Y coordinates in the X-Y coordinate system(step S207) and calculates the deviation amounts ΔX, ΔY of thatcelestial object image (step S209).

Subsequently, it is determined whether or not at least one of thecalculated deviation amount ΔX and the calculated deviation amount ΔYexceeds a corresponding predetermined threshold value (step S211).

If determining that at least one of the calculated deviation amount ΔXand the calculated deviation amount ΔY exceeds the correspondingpredetermined threshold value (if YES at step S211), the CPU 21calculates the rotational center deviation amounts Xd, Yd from thecalculated deviation amount ΔX, ΔY (step S213). Thereafter, from theserotational center deviation amounts Xd, Yd, the CPU 21 calculates theamount of deviation (error) ΔA between the theoretically-correctphotographing azimuth angle A and the photographing azimuth angle Asthat is input from the azimuth angle sensor 33 and the amount ofdeviation (error) Δh between the theoretically-correct photographingelevation angle h and the photographing elevation angle hs that is inputfrom the gravity sensor 35 (step S215). Thereafter, the CPU 21 correctsthe photographing azimuth angle As and the photographing elevation anglehs, which are respectively input from the azimuth angle sensor 33 andthe gravity sensor 35, with the deviation amounts ΔA and Δh (step S217).Namely, the CPU 21 obtains the accurate photographing azimuth angle A(i.e., As+ΔA) and the accurate photographing elevation angle h (i.e.,hs+Ah), in which the detection error thereof via the azimuth anglesensor 33 and the gravity sensor 35 have been corrected.

If it is determined at step S211 that neither of the calculateddeviation amount ΔX and the calculated deviation amount ΔY exceeds thecorresponding predetermined threshold value (if NO at step S211), theCPU 21 does not correct either the photographing azimuth angle As or thephotographing elevation angle hs, which are respectively input from theazimuth angle sensor 33 and the gravity sensor 35, and substitutes thephotographing azimuth angle As and the photographing elevation angle hsfor the accurate photographing azimuth angle A and the accuratephotographing elevation angle h, respectively (step S219). If apreliminary-tracking photographic image is obtained by performing acontinuous exposure during the preliminary auto-tracking photographingoperation (step S205) with the calculated deviation amount ΔX and thecalculated deviation amount ΔY being determined as not exceeding thecorresponding predetermined threshold value (if NO at step S211), it ispossible to display the preliminary-tracking photographic image (that isobtained by preliminary tracking operation (step S205)) as an actualimage on the LCD monitor 23, and to store this image data onto thememory card 25 as an image file of a predetermined format.

[Actual Photographing Operation]

The actual photographing operation (step S115) in the present embodimentwill be hereinafter discussed in detail with reference to the flow chartshown in FIG. 10.

In the actual photographing operation, first the CPU 21 calculates theactual-tracking drive control data (dA/dt, dh/dt, dθ/dt) based on thelatitude information ε that is input from the GPS unit 31 in thepreliminary photographing operation and either the accuratephotographing azimuth angle A and the accurate photographing elevationangle h which are obtained by correcting the photographing azimuth angleAs and the photographing elevation angle hs input in the preliminaryphotographing operation with the errors ΔA and Δh at step S217 or thephotographing azimuth angle As and the photographing elevation angle hsinput in the preliminary photographing operation which are thesubstitutions for the accurate photographing azimuth angle A and theaccurate photographing elevation angle h at step S219 (step S301).

Subsequently, the CPU 21 calculates a longest exposure time (exposuretime limit) Tlimit according to the actual-tracking drive control data(dA/dt, dh/dt, dθ/dt), the focal length information f that is input fromthe focal length detector 105 in the preliminary photographing operationand mechanical movement limits Lx, Ly and Lθ in the range of movement ofthe image sensor 13 that is moved by the image sensor drive unit 15(step S305).

Subsequently, the CPU 21 determines whether or not the exposure time T,which is arbitrarily set by the user, is within (less than or equal to)the longest exposure time Tlimit that is calculated at step S305 (stepS307). If the exposure time T is determined at step S307 as being withinthe longest exposure time Tlimit (if YES at step S307), the CPU 21 setsthe exposure time T as an exposure time for the celestial-objectauto-tracking photographing operation. On the other hand, if theexposure time T is determined at step S307 as exceeding the longestexposure time Tlimit (if NO at step S307), the CPU 21 sets the longestexposure time Tlimit as an exposure time for the celestial-objectauto-tracking photographing operation (step S309). Subsequently, the CPU21 controls the operation of a shutter (not shown) so that the shutteropens for the set exposure time to start capturing an image via theimage sensor 13 (step S311). Although an image is normally captured withthe diaphragm 103 fully open, the aperture size of the diaphragm 103 canbe arbitrarily set by the user.

Subsequently, until the set exposure time T elapses, the CPU 21continues the exposure operation while controlling the linear movementand the rotational movement of the image sensor 13 in accordance withthe calculated actual-tracking drive control data (dA/dt, dh/dt, dθ/dt)(step S317, NO at step S319). This makes capturing of a still image of acelestial object(s) possible in a state where each celestial objectappears stationary in long exposure astrophotography simply byperforming an exposure with the digital camera 10 fixed with respect tothe ground (earth). During this exposure time, the CPU 21 can calculateand update the actual-tracking drive control data (dA/dt, dh/dt, dθ/dt)based on the latitude information ε, the photographing azimuth angleinformation As and the photographing elevation angle information hs thatare input from the GPS unit 31, the azimuth angle sensor 33 and thegravity sensor 35, respectively (steps S217, S219, S313 and S315).

Subsequently, after a lapse of the exposure time T (YES at step S319),the CPU 21 closes the shutter (not shown) to terminate the exposureoperation (step S321). Thereafter, the CPU 21 reads out image data onthe captured image from the image sensor 13 (step S323) and performsimage processing operations such as a white balance adjustment operationand an image processing operation for converting the format type into apredetermined type of format (step S325). Lastly, the CPU 21 causes theimage data on the captured image, on which the aforementioned imageprocessing operations have been performed, to be displayed on the LCDmonitor 23, stores this image data into the memory card 25 as an imagefile of a predetermined format (step S327), and control returns.

As described above, according to the above described method ofautomatically tracking and photographing celestial objects, and aphotographic apparatus that employs this method, according the presentinvention, the preliminary-tracking drive control data (dAs/dt, dhs/dt,dθ/dt), which is for use in performing a preliminary tracking operation,is calculated based on the photographing azimuth angle information Asand the photographing elevation angle information hs; the firstpreliminary image and the second preliminary image, which respectivelycorrespond to the commencement point and the termination point of thepreliminary tracking operation are obtained; the amount of deviation(ΔX, ΔY) between the celestial object image in the first preliminaryimage and the corresponding celestial object image in the secondpreliminary image is calculated; from the amount of deviation, theactual-tracking drive control data (dA/dt, dh/dt, dθ/dt), which is foruse in performing an actual tracking operation, is calculated so as tocancell out the deviation amount (ΔX, ΔY); and the celestial-objectauto-tracking photographing operation is performed based on theactual-tracking drive control data. Accordingly, a high precisioncelestial-object auto-tracking photographing operation can be achievedby calculating the actual-tracking drive control data (dA/dt, dh/dt,dθ/dt) even if the input data on the photographing azimuth angle As andthe photographing elevation angle hs are low in accuracy, which makes itpossible to capture a still image of a celestial object(s) in a statewhere each celestial object appears stationary even in long exposureastrophotography.

In the above described embodiment, the image sensor drive unit 15physically linearly-moves the image sensor 13 and rotates the imagesensor 13 by drive control of the CPU 21. However, instead of physicallymoving the image sensor 13 in this manner, by partly trimming the entireimaging area of the image sensor 13 (i.e., the entire part of theimaging surface 14) electronically to define the remaining part(non-trimmed part) of the imaging area of the image sensor 13 as atrimmed imaging area, it is possible to perform an exposure whilelinearly moving this trimmed imaging area in directions orthogonal tothe optical axis LO of the photographing optical system 101 and rotatingthe trimmed imaging area about an axis parallel to the optical axis LOaccording to the actual-tracking drive control data (dA/dt, dh/dt,dθ/dt). In this manner, it is possible to perform an exposure whilelinearly moving the aforementioned trimmed imaging area in directionsorthogonal to the optical axis LO of the photographing optical system101 and rotating the trimmed imaging area about an axis parallel to theoptical axis LO by sending a trimming command signal to the image sensor13 periodically at a predetermined drive frequency by the CPU 21 in FIG.1.

Although the above described embodiment of the digital camera 10 isequipped with the image sensor drive unit 15 that moves the image sensor13 in directions orthogonal to an optical axis and rotates the imagesensor 13 about an axis parallel to this optical axis, the digitalcamera according to the present invention can be alternativelyconfigured even if the image sensor drive unit 15 is omitted andreplaced by a combination of an image shake corrector (anti-shakeapparatus) provided in the photographing lens 101 with an image shakecorrecting lens for moving object images on the image sensor 13 and animage sensor rotating mechanism for rotating the image sensor 13 or withthe aforementioned manner of electronically rotating the aforementionedtrimmed imaging area.

Obvious changes may be made in the specific embodiment of the presentinvention described herein, such modifications being within the spiritand scope of the invention claimed. It is indicated that all mattercontained herein is illustrative and does not limit the scope of thepresent invention.

What is claimed is:
 1. A method of automatically tracking andphotographing a celestial object which moves relative to a photographicapparatus due to diurnal motion so that an image of the celestial objectthat is formed on an imaging surface of an image sensor via aphotographing optical system of the photographic apparatus becomesstationary relative to a predetermined imaging area of the image sensorduring a celestial-object auto-tracking photographing operation, themethod comprising: obtaining azimuth information, with respect to thephotographic apparatus, of the celestial object; calculatingfirst-tracking drive control data for performing a first-trackingphotographing operation based on the azimuth information; performing thefirst-tracking photographing operation, during a predetermined exposuretime, based on the first-tracking drive control data; obtaining, afterthe first-tracking photographing operation based on the first-trackingdrive control data finishes, a first image, upon lapse of apredetermined time, and a second image, wherein the first image and thesecond image respectively correspond to a beginning and an ending ofimages taken by the first-tracking photographing operation; calculatingan amount of deviation between a celestial object image in the firstimage and a corresponding celestial object image in the second image;and judging, in accordance with a comparison between the deviationamount and a predetermined threshold value, whether a second-trackingphotographing operation is to be performed.
 2. The method according toclaim 1, wherein, when the second-tracking photographing operation is tobe performed, the method further comprises: calculating, based on theamount of deviation, second-tracking drive control data for performingthe second-tracking photographing operation with the deviation amountcancelled; and performing the second-tracking photographing operationbased on the second-tracking drive control data, and wherein calculatingsecond-tracking drive control data comprises correcting thefirst-tracking drive control data with the deviation amount to calculatethe second-tracking drive control data.
 3. The method according to claim1, wherein performing the first-tracking photographing operationcomprises performing an exposure operation while moving thepredetermined imaging area of the image sensor and the image of thecelestial object that is formed on the imaging surface of the imagesensor.
 4. The method according to claim 2, wherein calculatingsecond-tracking drive control data further comprises: correcting theazimuth information based on the deviation amount; and calculatingsecond-tracking drive control data for moving the predetermined imagingarea of the image sensor and the image of the celestial object that isformed on the imaging surface of the image sensor based on the correctedazimuth information.
 5. The method according to claim 2, furthercomprising: calculating the second-tracking drive control data by movingthe predetermined imaging area of the image sensor and the image of thecelestial object that is formed on the imaging surface of the imagesensor.
 6. The method according to claim 2, wherein the judgingcomprises determining whether the deviation amount exceeds thepredetermined threshold value, and wherein calculating second-trackingdrive control data comprises: correcting the first-tracking drivecontrol data to cancel the deviation amount, when the deviation amountis determined as exceeding the predetermined threshold value; andsetting the first-tracking drive control data to second-tracking drivecontrol data, when the deviation amount is determined as one not morethan the predetermined threshold value.
 7. The method according to claim1, wherein the first-tracking drive control data is for moving the imagesensor in directions orthogonal to an optical axis of the photographingoptical system and rotating the image sensor about an axis parallel tothe optical axis while performing an exposure operation.
 8. The methodaccording to claim 1, wherein the predetermined imaging area of theimage sensor is a trimmed imaging area which is formed by partlyelectronically trimming an entire imaging area of the image sensor, andwherein the first-tracking drive control data is for moving the trimmedimaging area in directions orthogonal to an optical axis of thephotographing optical system and rotating the trimmed imaging area aboutan axis parallel to the optical axis while performing an exposureoperation.
 9. The method according to claim 1, wherein thefirst-tracking photographing operation comprises performing an exposureoperation while moving the predetermined imaging area of the imagesensor and the image of the celestial object that is formed on theimaging surface of the image sensor.
 10. A photographic apparatus whichautomatically tracks and photographs a celestial object which movesrelative to the photographic apparatus due to diurnal motion so that animage of the celestial object that is formed on an imaging surface of animage sensor via a photographing optical system of the photographicapparatus becomes stationary relative to a predetermined imaging area ofthe image sensor during a celestial-object auto-tracking photographingoperation, the photographic apparatus comprising: an obtainer thatobtains azimuth information, with respect to the photographingapparatus, of the celestial object; a calculator that calculatesfirst-tracking drive control data for performing a first-trackingphotographing operation based on the azimuth information; a device thatperforms the first-tracking photographing operation, during apredetermined exposure time, based on the first-tracking drive controldata; a device that obtains, after the first-tracking photographingoperation based on the first-tracking drive control data finishes, afirst image, upon lapse of a predetermined time, and a second image,wherein the first image and the second image respectively correspond toa beginning and an ending of images taken by the first-trackingphotographing operation; a calculator that calculates an amount ofdeviation between a celestial object image in the first image and acorresponding celestial object image in the second image; and a judgerthat judges in accordance with a comparison between the deviation amountand a predetermined threshold value, whether a second-trackingphotographing operation is to be performed.
 11. The photographicapparatus according to claim 10, wherein, when the second-trackingphotographing operation is to be performed, the photographing apparatusfurther calculates, based on the amount of deviation, second-trackingdrive control data for performing the second-tracking photographingoperation with the deviation amount cancelled, and performs thesecond-tracking photographing operation based on the second-trackingdrive control data, and wherein calculating the second-tracking drivecontrol data comprises correcting the first-tracking drive control datawith the deviation amount to calculate the second-tracking drive controldata.
 12. The photographic apparatus according to claim 10, whereinperforming the first-tracking photographing operation comprisesperforming an exposure operation while moving the predetermined imagingarea of the image sensor and the image of the celestial object that isformed on the imaging surface of the image sensor.
 13. The photographicapparatus according to claim 11, wherein calculating second-trackingdrive control data comprises: correcting the azimuth information basedon the deviation amount; and calculating second-tracking drive controldata for moving the predetermined imaging area of the image sensor andthe image of the celestial object that is formed on the imaging surfaceof the image sensor based on the corrected azimuth information.
 14. Thephotographic apparatus according to claim 11, wherein, calculatingsecond-tracking drive control data further comprises moving thepredetermined imaging area of the image sensor and the image of thecelestial object that is formed on the imaging surface of the imagesensor.
 15. The photographic apparatus according to claim 11, whereinthe judging comprises determining whether the deviation amount exceedsthe predetermined threshold value, and calculating the second-trackingdrive control data comprises: correcting the first-tracking drivecontrol data to cancel the deviation amount, when the deviation amountis determined as exceeding the predetermined threshold value; andsetting the first-tracking drive control data to second-tracking drivecontrol data, when the deviation amount is determined as not more thanthe predetermined threshold value.
 16. The photographic apparatusaccording to claim 10, wherein the first-tracking drive control data isfor moving the image sensor in directions orthogonal to an optical axisof the photographing optical system and rotating the image sensor aboutan axis parallel to the optical axis while performing an exposureoperation.
 17. The photographic apparatus according to claim 10, whereinthe predetermined imaging area of the image sensor is a trimmed imagingarea which is formed by partly electronically trimming an entire imagingarea of the image sensor, and wherein the first-tracking drive controldata is for moving the trimmed imaging area in directions orthogonal toan optical axis of the photographing optical system and rotating thetrimmed imaging area about an axis parallel to the optical axis whileperforming an exposure operation.
 18. The photographic apparatusaccording to claim 10, wherein the first-tracking photographingoperation comprises performing an exposure operation while moving thepredetermined imaging area of the image sensor and the image of thecelestial object that is formed on the imaging surface of the imagesensor.
 19. The method according to claim 1, wherein the judging judgeswhether the first-tracking drive control data is to be corrected, beforecorrection is performed on the first-tracking drive control data usingthe deviation amount.
 20. The photographic apparatus according to claim10, wherein the judger judges whether the first-tracking drive controldata is to be corrected, before correction is performed on thefirst-tracking drive control data using the deviation amount.